Question

Name two vectors that are perpendicular to (4, -1).

A) (1, 4) and (-1, -4)
B) (-1, 4) and (1, -4)
C) (1, -4) and (-1, 4)
D) (-1, -4) and (1, 4)

Answer 1

To find vectors that are perpendicular to (4, -1), we can use the fact that the dot product of two perpendicular vectors is 0. The vectors that are perpendicular to (4, -1) are A) (1, 4) and (-1, -4).

Step-by-step explanation:

To find vectors that are perpendicular to (4, -1), we can use the fact that the dot product of two perpendicular vectors is 0. We can choose any vector (a, b) that satisfies the equation 4a + (-1)b = 0. Let's check the options:

A) (1, 4) and (-1, -4): 4(1) + (-1)(4) = 4 - 4 = 0, so it's perpendicular.

B) (-1, 4) and (1, -4): 4(-1) + (-1)(4) = -4 - 4 = -8, so it's not perpendicular.

C) (1, -4) and (-1, 4): 4(1) + (-1)(-4) = 4 + 4 = 8, so it's not perpendicular.

D) (-1, -4) and (1, 4): 4(-1) + (-1)(4) = -4 - 4 = -8, so it's not perpendicular.

Therefore, the vectors that are perpendicular to (4, -1) are A) (1, 4) and (-1, -4).